Basic research for systematization of self-organization paradigm

这项研究旨在解决一个具有挑战性的问题，即“什么样的非线性创造了秩序，什么样的普遍规则支配着这个过程”。我们对开放非线性系统进行了几次大规模的计算机模拟，得到了以下结果：我们关于秩序形成的工作假设得到了更充分的证实。也就是说，当能量从外部持续供应到一个开放的局部系统时，能量松弛是间歇性重复的，新的有组织的结构以间歇性的方式产生。间歇响应是系统非线性的一种反映。一旦有外部能量供给，系统就会变得不稳定，无法将供给的能量释放成其他形式的能量。然而，由于不稳定模态的增长率不一定与能量供应的增长率相匹配，因此系统中积累了多余的能量。系统的非线性发展最终导致突然的结构转变，以释放积累的剩余能量。换句话说，在开放非线性系统中，外部持续的能量供给暂时使系统达到过饱和（能量最大值）状态，系统结构过渡到新的局部最小能量状态。通过在等离子体流源和非线性反馈系统之间放置粘性薄层的模拟，得到了自组织场景的新发现。也就是说，我们发现一个边界层将外部能量源和自组织系统划分开来，它起着“膜”的作用，可以自我调节地控制来自外部的能量流入的量。对模拟结果的仔细研究使我们得出这样的结论：薄的粘性层，即“膜”，在自组织中表现出两个重要的功能，即a)自然选择和b)自组织结构的稳定。

This research is aiming at attacking a challenging problem of "what nonlineality creates order, and what universal rule governs the process." We have done several large scale computer simulations for open nonlinear systems, and obtained the following results.1. Our working hypothesis on the formation of order turns out to be more confirmed. Namely, when energy is supplied continuously from outside to an open local system, energy relaxation is intermittently repeated, and new organized structures are created in an intermittent fashion.2. Intermittent response is a reflection of the nonlinearity of the system. Upon supply of energy from outside, the system becomes unstable to release the supplied energy into other forms of energy. However, because the growth rate of the unstable mode dose not necessarily match the rate of energy supply, a surplus energy is accumulated in the system. The nonlinear development of the system gives rise eventually to a sudden structure transition to release the accumulated surplus energy. In other words, a supersaturated (energy maximum) state is realized temporarily in the open nonlinear system by the continuous energy supply from outside, and the system undergoes a structure transition to a new local minimum energy state.3. A new findings on the scenario of self-organization is obtained by a simulation in which a viscous thin layr is placed between a plasma flow source and a nonlinear feedback system. Namely, a boundary layr demarcating the outside energy source and the self-organizing system is found to play a role of a "membrane", that controls self-adjustably the amount of the energy influx from outside. Careful examination of the simulation results has led us to a conclusion that a thin viscous layr, a "membrane", exhibits two important functions in self-organization, i.e., a) natural selection and b) stabilization of self-organized structure.